Find all the value of `m` for which the equation `sin^2x-(m-3)sinx+m=0` has real roots.

Determine the value(s) of m for which the equation x^(2)+m(4x+m-1)+2=0 has real roots.

The value of m for which the equation x^(2)-x+m^(2)=0 has no real roots is given as

Find the value of k for which the quadratic equation 3x^(2)+kx+3=0 has real and equal roots.

Find the values of p fro which the qadratic equation 2x^(2)+px+8=0 has real roots.

Find the values of k for which the equation x^(2)-4x+k=0 has distinct real roots.

Find the value of m for which the quadratic equation , 3x^(2) + 10x + (m-3) = 0 has roots which are reciproal to each other.

The number of interal values of m for which the equation (1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0, has no ral roots is

Find all positive ontegers n for which the equation nx^(4)+4x+3=0 has a real root.

Number of integral values of 'a' for which the equation cos2x+3sin x+4sin^(2)x=a-3 has a real root is/are